System and method for noninvasively measuring ventricular stroke volume and cardiac output

ABSTRACT

A system for non-invasively measuring cardiac output, stroke volume, or both comprises a pulse oximeter, a data processor, and means for generating an output reporting measured one or more CO or SV values to a user. A method for non-invasively measuring cardiac output, stroke volume, or both comprises collecting plethysmographic waveform data of a patient, providing the plethysmographic waveform to a data processor, and calculating measured values for CO or SV. The data processor comprises a mathematical model of the cardiovascular system integrated in a dynamic state space model (DSSM).

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. Ser. No. 12/640,278filed Dec. 17, 2009, which is non-provisional of U.S. 61/171,802 filedApr. 22, 2009. This application is additionally related to the followingUS patent applications:

Ser. No. 12/796,512 filed Jun. 8, 2010, issued as U.S. Pat. No.9,060,722;

Ser. No. 13/096,845 filed Apr. 28, 2011, issued as U.S. Pat. No.9,173,574;

Ser. No. 13/096,876 filed Apr. 28, 2011, issued as U.S. Pat. No.9,275,171;

Ser. No. 13/096,904 filed Apr. 28, 2011; Ser. No.

Ser. No. 13/181,027 filed Jul. 12, 2011, issued as U.S. Pat. No.8,494,829;

Ser. No. 13/181,140 filed Jul. 12, 2011; and Ser. No.

Ser. No. 13/181,247 filed Jul. 12, 2011.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The U.S. Government may have certain rights to this invention pursuantto Contract Number IIP-0839734 awarded by the National ScienceFoundation.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates generally to apparatus, systems, andmethods for noninvasively measuring cardiac output (CO) and leftventricular stroke volume (SV). More specifically, the inventionincludes systems and methods that measure CO and/or SV usingplethysmographic waveform data collected by a pulse oximeter.

Description of Related Art

There has been a long felt need in the medical arts for a noninvasiveway to measure left ventricular stroke volume (SV) and cardiac output(CO). SV is the volume of blood pumped by the left ventricle of theheart with a single heart cycle. CO is the product of SV and hear rate(HR). SV and CO are important physiological parameters for a number ofmedical conditions, including congestive heart failure (CHF).

Patients being treated for heart failure are normally medicated withdrugs that regulate diuresis and heart muscle function. An important aimof drug therapy is to maintain a CO that is sufficient to perfusetissues with oxygenated blood. It is advantageous to use the lowestpossible doses of drugs to manage CHF because the drugs used produceunwanted side effects. To optimally manage the dosage and selection ofdrugs in the treatment of CHF, one must monitor CO to assess theefficacy of the drugs and dosages being administered and/or to monitorpatient compliance.

Currently, CO is measured using invasive techniques such as the Fickmethod, the Thermodilution method, and implantablemicroelectromechanical devices (MEMs), also called CardioMEMs. The Fickmethod involves the measurement of oxygen consumption and computing thearteriovenous difference using samples of arterial blood and mixedvenous blood from the pulmonary artery. The thermodilution methodmeasures the rate at which cold saline solution is diluted in the blood.Both of these methods are performed in a hospital setting because theyrequire the placement of a catheter in the pulmonary artery.Additionally, the use of a pulmonary artery catheter use may alsoincrease morbidity in critically ill patients. CardioMEMs are surgicallyimplanted into patients in a hospital setting and, once implanted,provide measurements of SV and CO that can be used to monitor patients.The implantation of the cardioMEMs device into the pulmonary artery,however, is expensive and is performed in a hospital setting andinvolves the risks associated with heart catheterization.

Less invasive techniques for measuring SV and CO include esophagealDoppler and transesophageal echocardiography. Esophageal Dopplermeasures blood flow velocity in the descending thoracic aorta using aflexible ultrasound probe that is inserted into the esophagus. The bloodflow velocity is combined with an estimate of the cross-sectional areaof the aorta estimated from the patient's age, height, and weight tocalculate SV and CO. This technique requires someone with technicalskill to insert an esophageal Doppler monitor, which must be properlyaligned with respect to the thoracic aorta to provide accuratemeasurements. Transesophageal echocardiography involves measuring SVusing flow velocity calculated from the area under the measured Dopplervelocity waveform at the pulmonary artery, the mitral valve, or theaortic valve. This technique requires a highly trained operator toposition and place the esophageal Doppler monitor. These procedures arenot truly noninvasive because accessing the esophagus is perceived bypatients as invasively uncomfortable.

Truly noninvasive methods, apparatus, and systems are needed that canmeasure SV and CO, preferably in the homes of patients without the needfor skilled caregivers. Pulse oximetry has been investigated for decadesas a possible tool for the noninvasive measurement of SV and CO. A pulseoximeter (PO) is a device that obtains photoplethysmography (PPG) data,which measures changes in blood volume within a tissue caused by thepulse of blood pressure through the vasculature in the tissue. The bloodvolume change is detected by measuring the amount of light transmittedor reflected to a sensor from a light source used to illuminate theskin. The shape of the PPG waveform varies with the location and mannerin which the pulse oximeter is contacted with the body. In addition toPPG data, a pulse oximeter measures peripheral oxygen saturation (SpO2).Most often, the device operates in a transmission mode in which twowavelengths of light are passed through a body part to a photodetector.Changes in absorbance at each of the wavelengths are measured, whichallow the determination of the absorbance due to pulsing arterial blood,excluding venous blood, skin, bone, muscle, and other tissues.Alternatively, reflectance pulse oximetry can be used. A typical pulseoximeter comprises a data processor and a pair of light-emitting diodes(LEDs) facing a photodiode. One LED produces red light having awavelength of 660 nm, the other infrared light having a wavelength of940 nm. Oxygenated hemoglobin absorbs more infrared light and less redlight than hemoglobin. The transmission signals fluctuate over timebecause of changes in the amount of arterial blood present in the tissuecaused by the blood pulse associated with each cycle of the heart. Theratio of red light measured to infrared light measured is calculated bythe processor and is converted by the processor to SpO2 using a lookuptable based on the Beer-Lambert law.

Awad et al. (J. Clinical Monitoring and Computing, 2006, 20:175-184)reports that researchers have been attempting to understand therelationship between central cardiac hemodynamics and the resultingmeasured peripheral waveforms. Awad et al. studied ear pulse oximeterwaveforms in order to understand the underlying physiology reflected inthese waveforms and to extract information about cardiac performance.Multi-linear regression analysis of ear plethysmographic waveformcomponents were used to estimate CO from the ear plethysmograph and itwas determined that ear plethysmographic width correlates with CO. Awadet al. does not suggest that this correlation allows pulse oximetry orplethysmographic data to be used to calculate SV or CO.

Natalini et al. (Anesth. Analg. 2006, 103:1478-1484) reports the use ofpulse oximetry to predict which hypotensive patients are likely torespond positively to increasing blood volume. Arterial blood pressurechanges during mechanical ventilation are reported as accuratelypredicting fluid responsiveness. Photoplethysmographic (PPG) waveformvariations measured by pulse oximetry showed a correlation with measuredpulse pressure variation values associated with fluid responsiveness butneither SV nor CO were calculated. Natilini does not indicate that SV orCO can be calculated using PPG data.

US 2013/0310669 discloses a method for determining mixed venous oxygensaturation (SvO2) using a photoplethysmography pulse oximeter (PPG PO)device that measures changes in pulmonary circulation using a lightsource and a light detector applied to the thoracic wall of a patient.The light source and the detector are separated by at least 15-20 mm sothat the region of illumination overlaps a portion of the pulmonarymicrocirculation beneath the PPG device. The contribution of circulationin the thoracic wall to the PPG signal must be assessed using anadditional detector and/or light source that is attached to the thoracicwall less than 8 mm apart. The SvO2 value can be used to calculate COusing the Fick method from the values of total oxygen consumption,arterial oxygen content and venous oxygen content. One drawback of thismethod is that the pulmonary microcirculation is surrounded by bone,muscle, and other tissues that make the contribution of circulation inthe thoracic wall to the PPG signal difficult to measure reliably.Another drawback is that the measured values depend on the accurateplacement of the light emitters and sensors, which may be difficult toreproduce for each subsequent measurement.

U.S. Pat. No. 9,289,133 discloses a method and apparatus for monitoringproportional changes in CO from a blood pressure signal measurementobtained by fingertip PPG. A time constant of the arterial tree isdefined as the product of the total peripheral resistance (TPR) and aconstant arterial compliance and is determined by analyzing long timescale variations of more than one cardiac cycle. A value proportional toCO is determined from the ratio of the blood pressure signal to theestimated time constant using Ohm's law. An invasive, absolute COcalibrating measurement is required to derive absolute CO values fromthe proportional CO change values obtained using PPG. This method andapparatus cannot measure values for SV or CO without an invasive COmeasurement and therefore requires a hospital setting and skilledmedical personnel.

WO 2010/0274102 A1 discloses a data processing method and associatedapparatus and systems that measures SV and CO from pulse oximetry data.The pulse oximeter system comprises a data processor configured toperform a method that combines a probabilistic processor and aphysiological model of the cardiovascular system in a DynamicState-Space Model (DSSM) that can remove contaminating noise andartifacts from the pulse oximeter sensor output and measure blood oxygensaturation, HR, SV, aortic pressure and systemic pressures. This pulseoximeter and associated method provides truly noninvasive measurement ofCO and SV suitable for monitoring patients with CHF. The DSSM comprisesa mathematical model of the cardiovascular system that models thephysiological processes which produce the pulses measured by the pulseoximeter. In one embodiment, the model comprises parameters includingaortic pressure, radial pressure, peripheral resistance, aorticimpedance, and blood density.

BRIEF SUMMARY OF THE INVENTION

The present invention fills a need in the art for truly noninvasiveapparatus and methods for measuring SV and CO by providing a system andmethod for measuring and reporting SV and/or CO using plethysmographic(PG) waveform data from a photoplethysomgraphic pulse oximeter (PPG PO).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart showing the path of information flow from abiomedical sensor to a data processor and on to an output displayaccording to one embodiment of the invention.

FIG. 2 is a flow chart showing inputs, outputs, and conceptual divisionof model parts for a dynamic state-space model (DSSM).

FIG. 3 is a block diagram showing mathematical representations ofinputs, output and conceptual divisions of the DSSM shown in FIG. 2.

FIG. 4 is a mathematical representation of the process of dualestimation.

FIG. 5 is a schematic diagram showing the process steps involved in adual estimation process.

FIG. 6 is a mathematical representation of the process of jointestimation.

FIG. 7 is a schematic diagram showing the process steps involved in ajoint estimation process.

FIG. 8 is a flow chart showing the components of a DSSM used for pulseoximetry data processing.

FIG. 9 is a flow chart showing examples of parameter inputs and outputsfor a DSSM used for pulse oximetry data processing.

FIG. 10 is a flow chart showing the components of a DSSM used forelectrocardiography data processing.

FIG. 11 is a chart showing input sensor data from a fingertip pulseoximeter and processed output data from a data processor configured toprocess pulse oximetry data.

FIG. 12 is a chart showing input sensor data from a fingertip pulseoximeter and processed output data from a data processor configured toprocess pulse oximetry data under a low blood perfusion condition.

FIG. 13 is a chart showing noisy non-stationary ECG sensor data inputand processed heart rate and ECG output for a data processor configuredto process ECG sensor data.

FIG. 14 is a chart showing input ECG sensor data and comparing outputdata from a data processor according to the present invention withoutput data generating using a Savitzky-Golay FIR data processingalgorithm.

DETAILED DESCRIPTION OF THE INVENTION

As used herein, “noninvasively” and “noninvasive” are used to indicatethat a method, system, or apparatus does not involve an invasive orminimally invasive procedure such as surgery or catheterization.Additionally, “noninvasively” and “noninvasive” are used to indicatethat a method, system, or apparatus does not involve endoscopy,phlebotomy, biopsy, or a procedure that requires intubation orartificial respiration.

FIG. 1 is a top-level schematic for data processing according to thepresent invention. A biomedical sensor, such as pulse oximeter, normallyproduces a raw analog output signal that is converted to a raw digitaloutput signal. The analog to digital conversion may also be accompaniedby signal filtering or conditioning. Digital signals are received by adata processor configured to process the digital data and produce aprocessed (or clean) signal comprising an estimated true value for thephysiological parameter being measured. The processed signal is thendisplayed, for example, in the form of an electronic, hard copy,audible, visual, and/or tactile output. The output may be used, forexample, by a user to monitor a patient, by a user for self monitoring,or by a user as biofeedback process.

The data processor shown in FIG. 1 is configured to receive, as inputdata, digital signals from one or more biomedical sensors, and enter thedata into a dynamic state-space model (DSSM) integrated with a processorengine. The integrated DSSM/processor engine produces transformed outputdata that may correspond to a physiological parameter measured by thebiomedical sensor(s), in the form of an estimated true value for thephysiological parameter. The processor engine may operate in a dualestimation mode (a dual estimation engine) or in a joint estimation mode(a join estimation engine). The output may include additional outputscorresponding to physiological parameters not measured by thephysiological sensor(s), diagnostic information, and a confidenceinterval representing the probability that the output estimated value(s)for the physiological parameter(s) is accurate. The data transformationprocess performed by the data processor may be used to remove artifactsfrom the input data to produce output data having higher accuracy thanthe input data and/or to extract information from the input data togenerate output data estimating the values for physiological parametersthat are not otherwise measured or reported using data from thesensor(s). In the case of a pulse oximeter, the physiologicalparameter(s) that are not otherwise measured may include SV, and/or CO.

Mathematical and Computational Models

A mathematical model or a computer model, as used herein, involves theuse of state parameters and model parameters in a mathematicalrepresentation of physiological processes that give rise to aphysiological parameter being measured and processes through whichsensor data is detected.

A mathematical model may include model and/or state parameters thatcorrespond directly to physiological parameters including vital signssuch as oxygen saturation of blood (SpO₂), heart rate (HR), respiratoryrate (RR), and blood pressure (BP) that can be directly measured;physiological parameters not directly measured such as total bloodvolume (TBV), left-ventricular stroke volume (SV), vasomotor tone (VT),autonomous nervous system (ANS) tone, and cardiac output (CO); andhemoglobin-bound complexes, concentrations of metabolic intermediates,and concentrations of drugs present in one or more tissues or organs.

While the scope of a mathematical model used in the context of thepresent invention cannot possibly encompass every single process ofhuman physiology, it should have the capacity to interpret the measuredobservable(s). For instance, if the intent is to processelectrocardiography (ECG) signals, a model describing the generation andpropagation of electrical impulses in the heart should be included.

The fusion of two or more biomedical signals follows the same principle.For instance, if the intent is to measure blood pressure waves andelectrocardiogram signals simultaneously, the use of a heart modeldescribing both the electrical and mechanical aspects of the organshould be used. Initially, the model may also accept manual data inputas a complement to data from sensors. Nonlimiting examples of manuallyentered data include food consumption over time vital signs, gender,age, weight, and height.

Non-physiological models may be included in and/or coupled to the DSSMin cases where non-biomedical signals are measured. For instance, onemay use non-biomedical measurements to enhance or complement biomedicalmeasurements. A non-limiting example is the use of accelerometer data toenhance motion artifact rejection in biomedical measurements. In orderto accomplish this, the physiological model is extended to describe bothmeasurements, which may include, in this example, cardiovascularcirculation at rest, at different body postures (standing, supine, etc),and in motion.

Dynamic State-Space Model

FIG. 2 and FIG. 3 show schematics of one embodiment of a dynamicstate-space model (DSSM) used in the processing of data according to thepresent invention. The DSSM comprises a process model F thatmathematically represents physiological processes involved in generatingone or more physiological parameters measured by a biomedical sensor anddescribes the state of the subject over time in terms of stateparameters. This mathematical model optimally includes mathematicalrepresentations accounting for process noise such as physiologicallycaused artifacts that may cause the sensor to produce a digital outputthat does not produce an accurate measurement for the physiologicalparameter being sensed. The DSSM also comprises an observational model Hthat mathematically represents processes involved in collecting sensordata measured by the biomedical sensor. This mathematical modeloptimally includes mathematical representations accounting forobservation noise produced by the sensor apparatus that may cause thesensor to produce a digital output that does not produce an accuratemeasurement for a physiological parameter being sensed. Noise terms inthe mathematical models are not required to be additive.

While the process and observational mathematical models F and H may beconceptualized as separate models, they are normally integrated into asingle mathematical model that describes processes that produce aphysiological parameter and processes involved in sensing thephysiological parameter. That model, in turn, is integrated with aprocessing engine within an executable program stored in a dataprocessor that is configured to receive digital data from one or moresensors and to output data to a display or other output formats.

FIG. 3 provides mathematical descriptions of the inputs and outputscorresponding to FIG. 2. Initially, values for state parameters,preferably in the form of a state vector x_(k), are received by the DSSMtogether with input model parameters W_(k). Process noise v_(k) andobservation noise n_(k) are also received by the DSSM, which updates thestate parameter vector and model parameter vector and produces an outputobservation vector y_(k). Once the model is initialized, the updatedstate vector x_(k+1), updated model parameters W_(k+!), andtime-specific sensor data are used as input for each calculation forsubsequent iterations, or time steps.

The DSSM is integrated in a dual estimation processing engine or a jointestimation processing engine. The most favored embodiment makes use of aDSSM built into a Sigma point Kalman filter (SPKF) or Sequential MonteCarlo (SMC) processing engine. Sigma point Kalman filter (SPKF), as usedherein, refers to the collective name used for derivativeless Kalmanfilters that employ the deterministic sampling based sigma pointapproach to calculate approximations of the optimal terms of theGaussian approximate linear Bayesian update rule, including unscented,central difference, square-root unscented, and square-root centraldifference Kalman filters. SMC and SPKF processing engines operate on ageneral nonlinear DSSM having the form:x _(k) =f(x _(k−1) ,v _(k−1) ;W)  (1)y _(k) =h(x _(k) ,n _(k) ;W)  (2)

A hidden system state, x_(k), propagates over time index, k, accordingto the system model, f. The process noise is v_(k−1), and W is thevector of model parameters. Observations, y_(k), about the hidden stateare given by the observation model h and n_(k) is the measurement noise.When W is fixed, only state estimation is required and either SMC orSPKF can be used to estimate the hidden states.

Unsupervised Machine Learning

Unsupervised machine learning, sometimes referred to as systemidentification or parameter estimation, involves determining thenonlinear mapping:y _(k) =g(x _(k) ;w _(k))  (3)where xk is the input, yk is the output, and the nonlinear map g(.) isparameterized by the model parameter vector W. The nonlinear map, forexample, may be a feed-forward neural network, recurrent neural network,expectation maximization algorithm, or enhanced Kalman filter algorithm.Learning corresponds to estimating W in some optimal fashion. In thepreferred embodiment, SPKF or SMC is used for updating parameterestimates. One way to accomplish this is to write a new state-spacerepresentationW _(k+1) =w _(k) +r _(k)  (4)d _(k) =g(x _(k) ;w _(k))+e _(k)  (5)where w_(k) correspond to a stationary process with identity statetransition matrix, driven by process noise r_(k). The desired outputd_(k) corresponds to a nonlinear observation on w_(k).Dual Estimation Engine for Estimation of State and Model Parameters

The state and parameter estimation steps may be coupled in an iterativedual-estimation mode as shown in FIGS. 4 and 5. This formulation for astate estimator operates on an adaptive DSSM. In the dual estimationprocess, states x_(k) and parameters W are estimated sequentially insidea loop. When used in a data processor for a pulse oximeter, the currentstate x_(k) from pulse oximeter sensor input y_(k). States x_(k), andparameters W are estimated sequentially inside a loop. Parameterestimates are passed from the previous iteration to state estimation forthe current iteration. Several different implementations or variants ofthe SMC and SPKF methods exist, including the sigma-point, Gaussian-sum,and square-root forms. The particular choice may be influenced by theapplication.

The current estimate of the parameters W_(k) is used in the stateestimator as a given (known) input, and likewise the current estimate ofthe state x_(k) is used in the parameter estimator. This results in astep-wise stochastic optimization within the combined state-parameterspace.

The flow chart shown FIG. 5 provides a summary of the steps involved indual estimation process. Initial probability distributions for state andmodel parameters are provided to the DSSM to produce an initialprobability distribution function (first PDF or prior PDF) representingthe initial state. Data for a time t₁ from a sensor (new measurement)and the initial PDF are combined using a Bayesian statistical process togenerate a second, posterior PDF that represents the state at the timeof the measurement for the first sensor data. Expectation values for thesecond PDF are calculated, which may represent the most likely truevalue. Expectation values may also represent, for instance, theconfidence interval or any statistical measure of uncertainty associatedwith the value. Based upon the expectation values, usually but notnecessarily the values for state parameters having the highestprobability of being correct, updated state parameters for time t₁ arecombined with sensor data for time t₁ to update the model parameters fortime t₂ in the DSSM by the process shown in FIG. 4. The expectationvalues are also fed into the DSSM as the state, in the form of a vectorof state parameters (new PDF) as shown in FIG. 4. Once the stateparameters and model parameters for the DSSM are updated to time t₁, theprocess is repeated with timed data for time t₂ to produce updatedparameters for time t₂ and so forth. The time interval between timesteps is usually constant such that time points may be described as t,t+n, t+2n, etc. If the time interval is not constant, then the time maybe described using two or more time intervals as t, t+n, t+n+m, etc.

Joint Estimation Engine for Estimation of State and Model Parameters

The state and parameter estimation steps may also be performed in asimultaneous joint-estimation mode as shown in FIGS. 6 and 7. Thecalculated variables for the state parameters and model parameters ofthe physiological model are concatenated into a singlehigher-dimensional joint state vector:

$\begin{matrix}{X = \begin{bmatrix}x_{k}^{T} & w_{k}^{T}\end{bmatrix}^{T}} & (6)\end{matrix}$where x_(k) are the state parameters and w_(k) the model parameters. Thejoint state space is used to produce simultaneous estimates of thestates and parameters.

The flow chart shown FIG. 7 provides a summary of the steps involved indual estimation process. The process is similar to that shown for dualestimation in FIG. 5, with the exception that model and state parametersare not separated into two separate vectors, but are representedtogether in a single vector. The process is initiated by entering avector representing initial state and model parameter valuedistributions into the DSSM and producing an initial first PDF. Thefirst PDF is combined with sensor data (new measurement) for time t₁ ina Bayesian statistical process to generate a second, posterior PDF thatrepresents the state and model parameters at time t₁. Expectation valuesfor the second PDF are calculated, which may represent the most likelytrue value. Expectation values may also represent, for instance, theconfidence interval or any statistical measure of uncertainty associatedwith the value. Based upon the expectation values, updated state andmodel parameters for time t₁ are entered into the DSSM by the processshown in FIG. 6. Once the state parameters and model parameters for theDSSM are updated to time t₁, the process is repeated with timed data fortime t₂ to produce updated parameters for time t₂ and so forth.

Compared to dual estimation, both state and model parameters areconcatenated into a single vector that is transformed by the DSSM.Hence, no machine learning step is necessary in order to update modelparameters. Joint estimation may be performed using a sequential MonteCarlo method or sigma-point Kalman method. These may take the form ofunscented, central difference, square-root unscented, and square-rootcentral difference forms. The optimal method will depend on theparticular application.

Sequential Monte Carlo Methods

SMC methods estimate the probability distributions of all the modelunknowns by propagating a large number of samples called probabilityparticles in accordance with the system models (typically nonlinear,non-Gaussian, non-stationary) and the rules of probability. Artifactsare equivalent to noise with short-lived probability distributions, alsocalled non-stationary distributions. The number of simulated particlesscales linearly with computational power, with 100 particles beingreasonable for real time processing with presently available processors.The system model describes pertinent physiology and the processor engineuses the system model as a “template” from which to calculate, usingBayesian statistics, posterior probability distribution functions(processed data). From this, the expectation values (e.g. the mean) andconfidence intervals can be estimated FIG. 7. The combination of SMCwith Bayesian Statistics to calculate posterior probability distributionfunctions is often referred to as a Particle Filter.

SMC process nonlinear and non-Gaussian problems by discretizing theposterior into weighted samples, or probability particles, and evolvingthem using Monte Carlo simulation. For discretization, Monte Carlosimulation uses weighted particles to map integrals to discrete sums:

$\begin{matrix}{{{p\left( x_{k} \middle| y_{1:k} \right)} \approx {\hat{p}\left( x_{k} \middle| y_{1:k} \right)}} = {\sum\limits_{i = 1}^{n}\;{\delta\left( {x_{k} - x_{k}^{(i)}} \right)}}} & (7)\end{matrix}$where the random samples {x(i); i=1, 2, . . . , N}, are drawn fromp(x_(k)|y_(1:k)) and δ(.) is the Dirac delta function. Expectations ofthe formE[g(x _(h))]=∫g(x _(h))p(x _(h) |y _(1:k))dx _(h)  (8)can be approximated by the estimate:

$\begin{matrix}{{{E\left\lbrack {g\left( x_{k} \right)} \right\rbrack} \approx {\overset{\sim}{E}\left\lbrack {g\left( x_{k} \right)} \right\rbrack}} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{g\left( x_{k}^{(i)} \right)}}}} & (9)\end{matrix}$if the distribution has finite support. As N approaches infinity, theestimate converges to the true expectation.

The optimal Bayesian solution can be outlined by the following recursivealgorithm. Suppose the required PDF a p(x_(k−1)|y_(t:k−1)) at time k−1is available. In the prediction stage, the prior PDF at time k isobtained using the DSSM via the Chapman-Kolmogorov equation:p(x _(k) |y _(1:k−1))=∫p(x _(h) |x _(k−1))p(x _(k−1) |y _(1:k−1))dx_(k−1)  (10)

The DSSM model describing the state evolution p(x_(k)|x_(k−1)) isdefined by the system equation (1) and the known statistics of v_(k−1).At time step k a measurement y_(k) becomes available, and this may beused to update the prior (updated stage) via Bayes' rule:

$\begin{matrix}{{p\left( x_{k} \middle| y_{1:k} \right)} = \frac{{p\left( y_{k} \middle| x_{k} \right)}{p\left( x_{k} \middle| y_{1:{k - 1}} \right)}}{p\left( y_{k} \middle| y_{1:{k - 1}} \right)}} & (11)\end{matrix}$where the normalizing constantp(y _(k) |y _(1:k−1))=∫p(y _(k) |x _(k))p(x _(k) |y _(1:k−1))dx_(k)  (12)depends on the likelihood function p(y_(k)|x_(k)) defined by themeasurement model (equation 2) and the known statistics of n_(k).

It is not possible to sample directly from the posterior densityfunction so importance sampling from a known proposal distributionπ(x_(0:k)|y_(1:k)) is used. One may use sigma-point Kalman filters, forexample, to generate the proposal.

The known distribution is introduced into Equation 5 to yield:

$\begin{matrix}{{E\left\lbrack {g\left( x_{0:k} \right)} \right\rbrack} = {\int{{g\left( x_{0:k} \right)}\frac{w_{k}\left( x_{0:k} \right)}{p\left( y_{1:k} \right)}{\pi\left( x_{0:k} \middle| y_{1:k} \right)}d\; x_{0:k}}}} & (13)\end{matrix}$where the variables w_(k)(x_(0:k)) are unnormalized importance weights,which are written as w_(k)(x_(0:k))=w_(k):

$\begin{matrix}{{w_{k}\left( x_{0:k} \right)} = \frac{{p\left( y_{1:k} \middle| x_{0:k} \right)}{p\left( x_{0:k} \right)}}{\pi\left( x_{0:k} \middle| y_{1:k} \right)}} & (14)\end{matrix}$resulting in a weighted expectation:

$\begin{matrix}{{{E\left\lbrack {g\left( x_{0:k} \right)} \right\rbrack} \approx {\overset{\sim}{E}\left\lbrack {g\left( x_{0:k} \right)} \right\rbrack}} = {\sum\limits_{i = 1}^{N}\;{{\overset{\sim}{w}}_{k}^{(i)}{g\left( x_{0:k}^{(i)} \right)}}}} & (15)\end{matrix}$where {tilde over (w)}_(h) ^((i)) are normalized importance weights:

$\begin{matrix}{{\overset{\sim}{w}}_{k}^{(i)} = {w_{k}^{(i)}/{\sum\limits_{j = 1}^{N}w_{k}^{(j)}}}} & (16)\end{matrix}$Importance sampling is made sequential by reiterating the Markov 1^(st)order assumption, resulting in the assumption that the current state isnot dependent on future observations:π(x _(0:h) |y _(1:h))=π(x _(0:h−1) |y _(1:k−1))π(x _(h) |x _(0:h−1) ,y_(1:h))  (17)and that observations are conditionally independent given the states:

$\begin{matrix}{{p\left( x_{0:k} \right)} = {{p\left( x_{0} \right)}{\prod\limits_{j = 1}^{k}\;{p\left( x_{j} \middle| x_{j - 1} \right)}}}} & (18) \\{{p\left( y_{1:k} \middle| x_{0:k} \right)} = {\prod\limits_{j = 1}^{k}{p\left( y_{j} \middle| x_{j} \right)}}} & (19)\end{matrix}$

A recursive estimate for the importance weights is:

$\begin{matrix}{w_{k} = {w_{k - 1}\frac{{p\left( y_{k} \middle| x_{k} \right)}{p\left( x_{k} \middle| x_{k - 1} \right)}}{\pi\left( {\left. x_{k} \middle| x_{0:{k - 1}} \right.,y_{1:k}} \right)}}} & (20)\end{matrix}$which is called Sequential Importance Sampling (SIS). SIS suffers fromdegeneracy so that, over a few iterations, all but one of the importanceweights will be zero, effectively removing a large number of samples. Toremedy this, samples with low importance weights may be eliminated whilehigh importance samples may be multiplied. One way to accomplish this isSampling-Importance Resampling (SIR), which involves mapping the Diracrandom measure{x _(h) ^((i)) ,{tilde over (w)} _(h) ^((i)) ;i=1, . . . N}  (21)into a measure with equal weights, 1/N:

$\begin{matrix}\left\{ {x_{k}^{(j)},{\frac{1}{N};{i = 1}},\ldots\mspace{11mu},N} \right\} & (22)\end{matrix}$

A pseudo-code for a generic SMC (also called bootstrap filter orcondensation algorithm) can be written as:

1. Importance sampling step. For i=1, . . . , N, do:x _(h) ^((i)) ˜p(x _(h) |x _(k−1) ^((i)))  i)samplew _(h) ^((i)) ˜w _(h-1) ^((i)) p(y _(h) |x _(h) ^((i)))  ii)evaluate{tilde over (w)} _(k) ^((i)) =w _(h) ^((i))/Σ_(j=1) ^(N) w _(h)^((i))  iii) normalize2. Importance resampling step

-   -   i) eliminate or multiply samples x_(h) ^((i)) according to        weights {tilde over (w)}_(h) ^((i)) to obtain N random samples        approximately distributed according to p(x_(h)|y_(1:h))    -   ii) For i=1, . . . N, set w_(h) ^((i))={tilde over (w)}_(h)        ^((i))=N⁻¹        3. Output    -   i) any expectation, for instance:

${\hat{x}}_{k} = {{E\left\lbrack x_{k} \middle| y_{1:k} \right\rbrack} \approx {\frac{1}{N}{\sum\limits_{i = 1}^{N}\; x_{h}^{(i)}}}}$SPKF may be used to approximate probability distributions. Assuming thatx has a mean x covariance P_(x), and dimension L, a set of 2L+1 weightedsigma-points, S_(i)={w_(i), X_(i)}, is chosen according to:

$\begin{matrix}\begin{matrix}{X_{0} = \overset{\_}{x}} \\{{X_{i} = {{\overset{\_}{x} + {\left( {h\sqrt{P_{x}}} \right)_{i}\mspace{14mu} i}} = 1}},\ldots\mspace{11mu},L} \\{{X_{i} = {{\overset{\_}{x} - {\left( {h\sqrt{P_{x}}} \right)_{i}\mspace{14mu} i}} = {L + 1}}},\ldots\mspace{11mu},{2L}} \\{w_{0}^{(m)} = \frac{h^{2} - L}{h^{2}}} \\{{w_{i}^{(m)} = {{\frac{1}{2h^{2}}\mspace{14mu} i} = 1}},\ldots\mspace{11mu},{2L}} \\{{w_{i}^{(o_{1})} = {{\frac{1}{4h^{2}}\mspace{14mu} i} = 1}},\ldots\mspace{11mu},{2L}} \\{{w_{i}^{(o_{1})} = {{\frac{h^{2} - 1}{4h^{4}}\mspace{14mu} i} = 1}},\ldots\mspace{11mu},{2L}}\end{matrix} & (23)\end{matrix}$where h is a scaling parameter. Each sigma-point is propagated throughthe DSSM to yield the posterior sigma-point set, Y_(i):Y _(i) =h(f(X _(i))),i=0, . . . 2L  (24)

From this, the posterior statistics are calculated using a procedureresembling the linear Kalman filter. For instance, for the unscentedKalman filter case, a SPKF variant, the time-update equations are:

$\begin{matrix}{{X_{k|{k - 1}}^{x}} = {f\left( {{X_{k - 1}^{x}},{X_{k - 1}^{x}},{u_{k - 1}}} \right)}} & (25) \\{{{\hat{x}}_{k}^{-}} = {\sum\limits_{i = 0}^{2L}\;{w_{i}^{(m)}X_{i,{k|{k - 1}}}^{x}}}} & (26) \\{{P_{x_{k}}^{-}} = {\sum\limits_{i = 0}^{2L}{{w_{i}^{(o)}\left( {{X_{i,{k|{k - 1}}}^{x}} - {{\hat{x}}_{k}^{-}}} \right)}\left( {{X_{i,{k|{k - 1}}}^{x}} - {{\hat{x}}_{k}^{-}}} \right)^{T}}}} & (27)\end{matrix}$and the measurement-update equations are:

$\begin{matrix}{Y_{k|{k - 1}} = {h\left( {{X_{k|{k - 1}}^{x}} - {X_{k - 1}^{x}}} \right)}} & (28) \\{{\hat{y}}_{k}^{-} = {\sum\limits_{i = n}^{2L}\;{w_{i}^{(m)}Y_{i,{k|{k - 1}}}}}} & (29) \\{P_{{\overset{\_}{y}}_{k}} = {\sum\limits_{i = 0}^{2L}{{w_{i}^{(o)}\left( {{Y_{i,{k|{k - 1}}}} - {{\hat{y}}_{k}^{-}}} \right)}\left( {{Y_{i,{k|{k - 1}}}} - {{\hat{y}}_{k}^{-}}} \right)^{T}}}} & (30) \\{P_{x_{k}y_{k}} = {\sum\limits_{i = 0}^{2L}{{w_{i}^{(o)}\left( {{X_{i,{k|{k - 1}}}^{x}} - {{\hat{x}}_{k}^{-}}} \right)}\left( {{Y_{i,{k|{k - 1}}}} - {{\hat{y}}_{k}^{-}}} \right)^{T}}}} & (31) \\{K_{k} = {P_{x_{k}y_{k}}P_{{\overset{\_}{y}}_{k}}^{- 1}}} & (32) \\{{\hat{x}}_{k} = {{\hat{x}}_{k}^{-} + {K_{k}\left( {y_{k} - {{\hat{y}}_{k}^{-}}} \right)}}} & (33) \\{P_{x_{k}} = {P_{x_{k}}^{-} - {K_{k}P_{{\overset{\_}{y}}_{k}}K_{k}^{T}}}} & (34)\end{matrix}$where x, v and n superscripts denote the state, process noise andmeasurement noise dimensions, respectively.

The mathematical structure for sequential Monte Carlo and SPKF representtwo examples of a family of probabilistic inference methods exploitingMonte Carlo simulation and the sigma point transform, respectively, inconjunction with a Bayesian statistical process.

SPKF are generally inferior to SMC but are computationally cheaper. LikeSMC, SPKF evolve the state using the full nonlinear DSSM, but representprobability distributions using a sigma-point set. This is adeterministic step that replaces the stochastic Monte Carlo step in theSMC. As a result, SPKF lose accuracy when posterior distributions departheavily from the Gaussian form, such as with bimodal or heavily-taileddistributions, or with strong nonstationary distributions such as thosecaused by motion artifacts in pulse oximeters. For these cases SMC aremore suitable.

SPKF yields higher-order accuracy than the extended Kalman filter (EKF)and its related variants with equal algorithm complexity, O (L²). SPKFreturns 2^(nd) order accuracy for nonlinear and non-Gaussian problems,and 3rd order for Gaussian problems. EKF has only 1^(st) order accuracyfor nonlinear problems. Both EKF and SPKF approximate statedistributions with Gaussian random variables (GRV). However, the EKFpropagates the GRV using a single measure (usually the mean) and the1^(st) order Taylor expansion of the nonlinear system. The SPKF, on theother hand, decomposes the GRV into distribution moments (sigma points)and propagates those using the unmodified nonlinear system. SPKFimplementation is simpler than EKF since it is derivativeless. That is,it uses the unmodified DSSM form, and therefore does not require lengthyJacobian derivations.

The data processing method is also capable of prediction because themethod can operate faster than real time measurements. At any given timeduring data processing, the measurement PDF, obtained either from SPKFor SMC, embodies all available statistical information up to that pointin time. It is therefore possible to march the system model forwards intime, for instance, using the same sequential Monte Carlo method, toobtain deterministic or stochastic simulations of future signaltrajectories. In this way, the future health status (physiologicalstate) of a patient can be predicted with attached probabilitiesindicating the confidence of each prediction.

Noise Adaptation

The data processing method may benefit from a noise adaptation method iftimed sensor data contains noise and/or artifact that changes itsspectral qualities over time. That is, if timed sensor data has anon-stationary probability distribution function. Here, a knownalgorithm such as the Robins-Monro or Annealing methods may be added tothe data processing method in order to adapt the probabilitydistribution functions of noise terms (stochastic terms) in the DSSMaccording to changing noise and artifact present in sensor data.

Output

In general, the output may include estimates of the true measuredsignals (i.e. processed data), and estimates of values for one or morephysiological parameters measured by one or more sensors from which datawas received, and estimates of values for one or more physiologicalparameters not measured by the sensors from which data was received(data extraction). A state parameter estimate is the processed data fromthe physiological sensor. Both noise and artifacts can be attenuated orrejected even though they may have very distinct probabilitydistribution functions and may mimic the real signal. A model parameterestimate may be also used to produce a physiological parameter. Forexample, an estimate of total blood volume may be used to diagnosehemorrhage or hypovolemia. An estimate of tissue oxygen saturation mayindicate poor tissue perfusion and/or hypoxia. Estimates of glucoseuptake in several tissues may differentiate between diabetes mellitustypes and severities; and estimates of carotid artery radius may beindicative of carotid artery stenosis.

EXAMPLES

Pulse Oximeter with Probabilistic Data Processing

FIG. 8 shows the components of a DSSM suitable for processing data froma pulse oximeter, including components required to describe processesoccurring in a subject. FIG. 9 illustrates the DSSM broken down intoprocess and observation models, and including input and outputvariables. Heart rate (HR), stroke volume (SV) and whole-blood oxygensaturation (SpO₂) are estimated from input noisy red and infraredintensity ratios (R). Radial (Pw) and aortic (Pao) pressures are alsoavailable as state estimates.

In this example, the DSSM comprises the following function to representCO:

$\begin{matrix}{{Q_{CO}(t)} = {{\overset{\_}{Q}}_{CO}{\sum\limits_{k = 1}^{5}\;{a_{k}{\exp\left\lbrack \frac{- \left( {\underset{\_}{t} - b_{k}} \right)^{2}}{c_{k}^{2}} \right\rbrack}}}}} & (31)\end{matrix}$wherein CO Qco(t), is expressed as a function of HR and SV and whereQ_(CO)=(HR×SV)/60. The CO function pumps blood into a Windkessel3-element model of the vascular system including two state parameters:aortic pressure, Pao, and radial (Windkessel) pressure, P_(W):

$\begin{matrix}{P_{w,{k + 1}} = {{\frac{1}{C_{w}R_{p}}\;{\left( {{\left( {R_{p} + Z_{o}} \right)Q_{CO}} - P_{{co},k}} \right) \cdot \delta}\; t} + P_{w,k}}} & (32) \\{P_{{co},{k + 1}} = {P_{w,{k + 1}} + {Z_{o}Q_{CO}}}} & (33)\end{matrix}$R_(P) and Z_(O) are the peripheral resistance and characteristic aorticimpedance, respectively. The sum of these two terms is the totalperipheral resistance due to viscous (Poiseuille-like) dissipation:Z _(o)=√{square root over (ρ/AC ₁)}  (34)where ρ is blood density. The elastic component due to vessel complianceis a nonlinear function including thoracic aortic cross-sectional area,A:

$\begin{matrix}{{A\left( P_{co} \right)} = {A_{\max}\left\lbrack {\frac{1}{2} + {\frac{1}{\pi}\arctan\left( \frac{P_{co} - P_{0}}{P_{1}} \right)}} \right\rbrack}} & (35)\end{matrix}$where Amax, P₀ and P₁ are fitting constants correlated with age andgender:A _(max)=(5.62−1.5(gender))·cm²  (36)P ₀=(76−4(gender)−0.89(age))·mmHg  (37)P ₁=(57−0.044(age))·mmHg  (38)

The time-varying Windkessel compliance, Cw, and the aortic complianceper unit length, Cl, are:

$\begin{matrix}{C_{w} = {{l} = {{l\frac{d\; A}{d}} = {l\frac{A_{\max}/\left( {\pi\; P_{1}} \right)}{1 + \left( \frac{- P_{0}}{P_{1}} \right)^{2}}}}}} & (39)\end{matrix}$where l is the aortic effective length. The peripheral resistance isdefined as the ratio of average pressure to average flow. A set-pointpressure, Pset, and the instantaneous flow:

$\begin{matrix}{R_{P} = \frac{P_{set}}{\left( {{HR} \cdot {SV}} \right)/60}} & (40)\end{matrix}$are used to provide compensation autonomic nervous system responses. Thevalue for Pset is adjusted manually to obtain 120 over 75 mmHg for ahealthy individual at rest.

The compliance of blood vessels changes the interactions between lightand tissues with pulse. This is accounted for using a homogenous photondiffusion theory for a reflectance or transmittance pulse oximeterconfiguration. For the reflectance case:

R = = Δ ⁢ ⁢ I I = 3 2 ⁢ Σ a ′ ⁢ K ⁡ ( α , d , r ) ⁢ ∑ a art ⁢ Δ ⁢ ( 41 )for each wavelength. In this example, the red and infrared bands arecentered at ˜660 nm and ˜880 nm. l denotes the detected intensities:total reflected (no subscript), and the pulsating (ac) and background(dc) components. Va is the arterial blood volume, which changes as thecross-sectional area of illuminated blood vessels, ΔA_(w), changes as:ΔV _(a) ≈r·ΔA _(w)  (42)where r is the source-detector distance. The tissue scatteringcoefficient, Σs′, is assumed constant but the arterial absorptioncoefficient, Σa^(art), depends on blood oxygen saturation, SpO₂:

= H ⁡ [ Sp ⁢ O 2 · σ a 100 ⁢ % + ( 1 - Sp ⁢ O 2 ) · σ a 0 ⁢ % ] ( 43 )which is the Beer-Lambert absorption coefficient, with hematocrit, H,and red blood cell volume, v_(i). The optical absorption cross sectionsfor red blood cells containing totally oxygenated (HbO₂) and totallydeoxygenated (Hb) hemoglobin are σ_(a) ^(100%) and σ_(a) ^(0%),respectively.

The function K(α,d,r) contains, along with the scattering coefficient,the wavelength, sensor geometry and oxygen saturation dependencies thatalter the effective optical path lengths:

$\begin{matrix}{{K\left( {\alpha,d,r} \right)} \approx \frac{- r^{2}}{1 + {\alpha\; r}}} & (44)\end{matrix}$

The attenuation coefficient α is:α×3Σ_(a)(Σ_(s)+Σ_(a))  (45)where Σ_(a) and Σ_(s) are whole-tissue absorption and scatteringcoefficients, respectively, which are calculated from Mie Theory.

Red and infrared K values as a function of SpO₂ may be represented bytwo linear fits:K _(r)≈−4.03·SpO₂−1.17  (46)K _(ir)≈0.102·SpO₂−0.753  (47)in mm². The overbar denotes the linear fit of the original function. Thepulsatile behavior of ΔAw, which couples optical detection with thecardiovascular system model, is:

$\begin{matrix}{{\Delta\; A_{w}} = {\frac{A_{w,\max}}{\pi}\frac{P_{w,1}}{P_{w,1}^{2} + \left( {P_{w,{k + 1}} - P_{w,0}} \right)^{2}}\Delta\; P_{w}}} & (48)\end{matrix}$with P_(w,0)=(⅓)P₀ and P_(w,1)=(⅓)P₁ to account for the poorercompliance of arterioles and capillaries relative to the thoracic aorta.Third and fourth state variables, the red and infrared reflectedintensity ratios, R=lac/ldc, are:R _(r,k+1) =cΣ′ _(s,r) K _(r)Σ_(a,r) ^(art) ΔA _(w) +R_(r,k)+ν_(r)  (49)R _(ir,k+1) =cΣ′ _(s,ir) K _(ir)Σ_(a,ir) ^(art) ΔA _(w) +R_(ir,k)+ν_(ir)  (50)

Here, ν are Gaussian-distributed process noises intended to capture thebaseline wander of the two channels. The constant c subsumes all factorscommon to both wavelengths and is treated as a calibration constant. Theobservation model adds Gaussian-distributed noises, n, to R_(r) andR_(ir):

$\begin{matrix}{\begin{bmatrix}y_{r,k} \\y_{{ir},k}\end{bmatrix} = {\begin{bmatrix}R_{r,k} \\R_{{ir},k}\end{bmatrix} + \begin{bmatrix}n_{r,k} \\n_{{ir},k}\end{bmatrix}}} & (51)\end{matrix}$

A calibration constant c was used to match the variance of the reallac/ldc signal with the variance of the DSSM-generated signal for eachwavelength. After calibration, the age and gender of the patient wasentered. Estimates for the means and covariances of both state andparameter PDFs were entered. FIG. 11 plots estimates for a 15 s stretchof data. Photoplethysmographic (PPG) waveforms (A) were used to extractheart rate (B), SV (C), CO (D), blood oxygen saturation (E), and aorticand systemic (radial) pressure waveforms (F). Results of processingpulse oximetry at low blood perfusion are shown in FIG. 12. Lowsignal-to-noise PPG waveforms (A) were used to extract heart rate (B),SV (C), blood oxygen saturation (D), and aortic and systemic (radial)pressure waveforms (E).

Electrocardiograph with Probabilistic Data Processing

FIG. 10 is a schematic of a DSSM suitable for processingelectrocardiograph data, including components required to describe theprocesses occurring in a subject. The combination of SPKF or SMC instate, joint or dual estimation modes can be used to filterelectrocardiography (ECG) data. Any physiology model adequatelydescribing the ECG signal can be used, as well as any model of noise andartifact sources interfering or contaminating the signal. Onenon-limiting example of such a model is the ECG signal generatorproposed by McSharry (IEEE Transactions on Biomedical Engineering, 2003.50(3):289-294). Briefly, this model uses a sum of Gaussians withamplitude, center and standard deviation, respectively, for each wave(P, Q, R, S, T−, T+15) in an ECG. The observation model comprises thestate plus additive Gaussian noise, but more realistic pink noise or anyother noise distributions can be used.

FIG. 13 shows the results of processing a noisy non-stationary ECGsignal. Heart rate oscillations representative of normal respiratorysinus arrhythmia are present in the ECG. The processor accomplishesaccurate, simultaneous estimation of the true ECG signal and heart ratethat follows closely the true values. The performance of the processorin a noise and artifact-corrupted signal is shown in FIG. 14. A cleanECG signal representing one heart beat (truth) was contaminated withadditive noise and an artifact in the form of a plateau at R and S peaks(beginning at time=10 s). Estimates by the processor remain close to thetrue signal despite the noise and artifact.

While a specific DSSMs and input and output parameters are provided forthe purpose of describing the present method, the present invention isnot limited to the DSSMs, sensors, biological monitoring devices,inputs, outputs, except as defined by the following claims.

The invention claimed is:
 1. A system for non-invasively measuring leftventricular stroke volume (SV) and/or cardiac output (CO) of a patient,said system comprising: a pulse oximeter, a data processor, and meansfor generating an output reporting a measured SV or CO value to a userwherein: the pulse oximeter is configured to collect plethysmographicwaveform data of the patient and to transmit the plethysmographicwaveform data to the data processor; the data processor is configured toreceive said plethysmographic waveform data and comprises software thatcalculates the measured value for SV and/or CO using saidplethysmographic waveform data and reports the measured value for SVand/or CO to the user; the software that calculates a measured value forSV and/or CO from plethysmographic waveform data comprises aprobabilistic processor and a mathematical model of a cardiovascularsystem integrated in a dynamic state space model (DSSM); and themathematical model of the cardiovascular system comprises aorticpressure, radial pressure, peripheral resistance, aortic impedance,heart rate, stroke volume, and blood density as state or modelparameters.
 2. The system of claim 1, wherein the pulse oximeter isconfigured to collect plethysmographic waveform data of the patient andto transmit the plethysmographic waveform data to the data processor inreal time.
 3. The system of claim 1, wherein the software calculates themeasured value for SV and/or CO in real time.
 4. The system of claim 1,wherein the DSSM is integrated with a dual estimation processor engineor a joint estimation processor engine.
 5. The system of claim 1,wherein the means for generating an output reporting measured SV or COvalues to a user comprises means for generating an electronic display, ahard copy display, an audible sound, a visual display, or a tactileoutput.
 6. The system of claim 1, wherein the pulse oximeter is afingertip pulse oximeter.
 7. The system of claim 1, wherein themathematical model of a cardiovascular system includes model and/orstate parameters that correspond directly to one or more of peripheralblood oxygen saturation (SpO₂), heart rate (HR), respiratory rate (RR),and blood pressure (BP).
 8. The system of claim 7, wherein the dataprocessor is additionally configured to receive data from a directmeasurement of one or more of SpO₂, HR, RR, and BR.
 9. The system ofclaim 1, further comprising a blood pressure measuring device thattransmits blood pressure data to the processor and wherein the processorreceives said blood pressure data to be used as input into thecardiovascular model.
 10. The system of claim 1, wherein the processorcomprises a processing engine within an executable program that isconfigured to receive digital data from the pulse oximeter and to outputstroke volume data and/or cardiac output data to a display.
 11. Thesystem of claim 1, wherein: the DSSM receives first probabilitydistributions for state and model parameters to produce a firstprobability distribution function (PDF) representing a first state; datafor a time t1 from the pulse oximeter and the first PDF are combinedusing a Bayesian statistical process to generate a second PDF thatrepresents a state at time t1; expectation values for the second PDF arecalculated and, using the expectation values, updated state parametersfor time t1 are combined with pulse oximeter data for time t1 to updatethe model parameters for time t2 in the DSSM; expectation values arealso entered into the DSSM as the state, in the form of a vector ofstate parameters; after the state parameters and model parameters forthe DSSM are updated to time t1, the process is repeated with pulseoximeter data for time t2 to produce updated parameters for time t2; andthe processor is configured to process the parameters to generate anoutput related to ventricular stroke volume.
 12. The system of claim 11,wherein the state parameters and model parameters are concatenated intoa single vector that is transformed by the DSSM.